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In a Regular Pentagon Abcde, Inscribed in a Circle; Find Ratio Between Angle Eda and Angle Adc. - Mathematics

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Question

In a regular pentagon ABCDE, Inscribed in a circle; find ratio between angle EDA and angle ADC.

Solution

Arc AE subtends ∠AOE at the centre and
 ∠ADE at the remaining part of the circle.

∴ ∠ADE  =` 1/2 xx 72°`
               = 36                   [central angle is a regular pentagon at O]
∠ADC = ∠ADB + ∠BDC
= 36° + 36° + 72°
   ∴ ∠ADE : ∠ADC = 36° : 72° = 1: 2

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(B) | Q: 6 | Page no. 265
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In a Regular Pentagon Abcde, Inscribed in a Circle; Find Ratio Between Angle Eda and Angle Adc. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
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